Related papers: A Witt type formula
In this note we give a combinatorial characterization of all the unmixed bipartite graphs.
We present two hypermatrix formulations of the Cayley Hamilton theorem. One of the proposed formulation naturally extends to hypermatrices the combinatorial interpretations of the classical Cayley Hamilton theorem. We conclude by discussing…
We classify all the pairs of a commutative associative algebra with an identity element and its finite-dimensional commutative locally-finite derivation subalgebra such that the commutative associative algebra is derivation-simple with…
We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…
We apply some basic notions from combinatorial topology to establish various algebraic properties of edge ideals of graphs and more general Stanley-Reisner rings. In this way we provide new short proofs of some theorems from the literature…
In this paper, we give a class of reconstructible graphs.
We study a class of complex polynomial equations on a finite graph with a view to understanding how holistic phenomena emerge from combinatorial structure. Particular solutions arise from orthogonal projections of regular polytopes,…
We give a construction of Kirchberg algebras from graphs. By using product graphs in the construction we are able to provide models for general (UCT) Kirchberg algebras while maintaining the explicit generators and relations of the…
The graph algebra is a commutative, cocommutative, graded, connected incidence Hopf algebra, whose basis elements correspond to finite simple graphs and whose Hopf product and coproduct admit simple combinatorial descriptions. We give a new…
In this paper we would like to introduce some new methods for studying magic type-colorings of graphs or domination of graphs, based on combinatorial spectrum on polynomial rings. We hope that this concept will be potentially useful for the…
The definition and main properties of the Ihara zeta function for graphs are reviewed, focusing mainly on the case of periodic simple graphs. Moreover, we give a new proof of the associated determinant formula, based on the treatment…
The paper deals with some spectral properties of (mostly infinite) quantum and combinatorial graphs. Quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics, nanotechnology, optics, and…
The concept of diagrammatic combinatorial Hopf algebras in the form introduced for describing the Heisenberg-Weyl algebra in~\cite{blasiak2010combinatorial} is extended to the case of so-called rule diagrams that present graph rewriting…
In this paper, a function on any pair of graphs is defined whose properties are similar to the properties of dot product in vector space. This function enables us to define graph orthogonality and, also, a new metric on isomorphism classes…
In this article, we give a new class of automorphisms of Leavitt path algebras of arbitrary graphs. Consequently, we obtain Anick type automorphisms of these Leavitt path algebras and new irreducible representations of Leavitt algebras of…
In this article we introduce the {\it cylindrical construction} for graphs and investigate its basic properties. We state a main result claiming a weak tensor-like duality for this construction. Details of our motivations and applications…
We study some versions of the statement of Hadwiger's conjecture for finite as well as infinite graphs.
The paper investigates relationship between algebraic expressions and graphs. We consider a digraph called a Fibonacci graph which gives a generic example of non-series-parallel graphs. Our intention in this paper is to simplify the…
We use purely combinatorial arguments to give a formula to compute all graded Betti numbers of path ideals of line graphs and cycles. As a consequence we can give new and short proofs for the known formulas of regularity and projective…
The Witt ring of a complex flag variety describes the interesting -- i.e. torsion -- part of its topological KO-theory. We show that for a large class of flag varieties, these Witt rings are exterior algebras, and that the degrees of the…